Solid StatehardNUMERICAL

In a hypothetical cubic unit cell, identical atoms are present at all corners and precisely at all eSolid State Chemistry Question

Question

In a hypothetical cubic unit cell, identical atoms are present at all $8$ corners and precisely at all $12$ edge centers. What is the effective number of atoms ($Z$) in this unit cell?

Answer: 4

💡 Solution & Explanation

Contribution from corners = $8 \times (1/8) = 1$. A cube has 12 edges, and each edge is shared by 4 unit cells. Contribution from edge centers = $12 \times (1/4) = 3$. Total effective atoms ($Z$) = $1 + 3 = 4$.

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